Lin Weng

Iku Nakamura

Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.

Arithmetic Geometry And Number Theory

Masanobu Kaneko

This invaluable volume collects papers written by many of the world''s top experts on L -functions. It not only covers a wide range of topics from algebraic and analytic number theories, automorphic forms, to geometry and mathematical physics, but also treats the theory as a whole. The contributions reflect the latest, most advanced and most important aspects of L- functions. In particular, it contains Hida''s lecture notes at the conference and at the Eigenvariety semester in Harvard University and Weng''s detailed account of his works on high rank zeta functions and non-abelian L -functions. Sample Chapter(s). Chapter 1: Quantum Maass Forms (435 KB). Contents: Quantum Maass Forms (R Bruggeman); o-invariant of p -Adic L -Functions (H Hida); Siegel Modular Forms of Weight Three and Conjectural Correspondence of Shimura Type and Langlands Type (T Ibukiyama); Convolutions of Fourier Coefficients of Cusp Forms and the Circle Method (M Jutila); On an Extension of the Derivation Relation for Multiple Zeta Values (M Kaneko); On Symmetric Powers of Cusp Forms on GL 2 (H H Kim); Zeta Functions of Root Systems (Y Komori et al.); Sums of Kloosterman Sums Revisted (Y Motohashi); The LindelAf Class of L -Functions (K Murty); A Proof of the Riemann Hypothesis for the Weng Zeta Function of Rank 3 for the Rationals (M Suzuki); Elliptic Curves Arising from the Spectral Zeta Function for Non-Commutative Harmonic Oscillators and o 0 (4)-Modular Forms (K Kimoto & M Wakayama); A Geometric Approach to L -Functions (L Weng). Readership: Graduate students, lecturers, and active researchers in various branches of mathematics, such as algebra, analysis, geometry and mathematical physics."

Lin Weng

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